Is changing the diameter of the first stage within the rules? And what 2nd stage engine(s) can be used?
It was never clear to me at what point the parachute recovery option failed. ISTM that the reentry burn could be done on an F1 with a low throttle setting, requiring replacing the landing burn with a parachute. A bouncy castle seems out of the question, so it would have to survive a dunk in the salt water. Perhaps an inflatable at the base combined with pressurized tanks so it lands on its engine and tilts to float on its side with with engine out of the water?Those seem like surmountable problems to me. S2 really has to stay a Kestrel or it isn't an F1 anymore. S2 won't be recoverable, but will be cheap.Iridium is probably a good measure. Could their sats go up on dedicated launches for a similar price? Could F1 compete with Electron? If not then it probably isn't a viable alternative.
IMO the main point is to build a recoverable single engine Falcon. An expendable rocket probably won't compete.(Please respect the previous discussion of the existence or non-existence of "end of life" Merlin engines and don't rehash it.)
About EOL, at some point they will have to decide to withdraw engines from the reuse loop, so non-existence can be true now but not necessarily true in few years.Probably the F1 is not a priority for SpaceX but I imagine that a spin off company could manage the small launcher and keep it out of the main SpaceX activities. It would succeed or fail without affecting the parent.
It's also plausible EOL for engines may happen not when they hit a cycle limit, but when BFR starts to work well enough to convince everyone to move over.
It is possible, personally I doubt that something so huge like BFR/S can be a single solution for all problems, I think there will still be use cases where the F9 would fit better even if not fully recoverable.Launch a huge number of satellites to build a constellation is a thing, launching commercial sats is something different, F9 is here to stay for a long time IMHO.